The invention relates to a method and a device for the determination of the instantaneous mass flow with pulsating flows.
An analytical solution for any pulsating flows is known from Uchida, S. 1956, “The Pulsating Viscous Flow Superposed on the Steady Laminar Motion of Incompressible Fluid in a Circular Pipe,” J. Appl. Mat. Phys. (ZAMP), Vol. 7, pp. 403-422.
Durst et al., “Measurement of Instantaneous Flow Rates in Periodically Operating Injection Systems” Experiments in Fluids 20 (1996), pp. 178-188 has shown that the analytical solution of Uchida for the measurement of the velocity of the pulsating flow in the axis of a pipe via Laser Doppler Anemometry (LDA) can be used. A measuring method based on these findings is, for example, also described in U.S. Pat. No. 6,510,842 B2.—However, the methods which are based on the principle of LDA are also disadvantageous in several respects. The analytical solution contains Bessel functions whose solution requires a high degree of computation work in actual practice. A continuous measurement of a periodically pulsating flow is not possible with this. The provision of a device for the performance of the LDA is expensive. Apart from this, such a device is sensitive, in particular sensitive to oscillations, and is not suitable for the control or regulation of injection devices for motor vehicles.
Ray S., et al., 2005, “Mass Flow Rate Controlled Fully Developed Laminar Pulsating Pipe Flows,” Journal of Fluids Engineering, Vol. 127, pp. 1-13 discloses a further analytical solution using dimensionless numbers. This can be used to avoid the time-consuming calculation of the Bessel functions.
Object of the invention is to eliminate the disadvantages as per the state of technology. In particular, a method and a device are to be specified with which the instantaneous mass flow of periodically pulsating flows can be determined with an improved time-resolution. In accordance with a further goal of the invention, the method is to be accomplishable with a device being as robust and inexpensive as possible. In particular, continuous measurement of periodically oscillating flows such as occur with injection units for motor vehicles is to be possible.
This object is solved by the features of claims 1 and 11. Useful embodiments of the invention result from the features of claims 2 to 10 and 12 to 24.